This paper deals with a Skorokhod's integral based least squares type estimator $\widehat\theta_N$ of the drift parameter $\theta_0$ computed from $N\in\mathbb N^*$ (possibly dependent) copies $X^1,\dots,X^N$ of the solution $X$ of $dX_t =\theta_0b(X_t)dt +\sigma dB_t$, where $B$ is a fractional Brownian motion of Hurst index $H\in (1/3,1)$. On the one hand, some convergence results are established on $\widehat\theta_N$ when $H = 1/2$. On the other hand, when $H\neq 1/2$, Skorokhod's integral based estimators as $\widehat\theta_N$ cannot be computed from data, but in this paper some convergence results are established on a computable approximation of $\widehat\theta_N$.

翻译：本文研究基于斯柯罗霍德积分的漂移参数$\theta_0$的最小二乘型估计量$\widehat\theta_N$，该估计量由$N\in\mathbb N^*$个（可能相关的）解过程$X$的样本$X^1,\dots,X^N$计算得到，其中$X$满足$dX_t =\theta_0b(X_t)dt +\sigma dB_t$，$B$为赫斯特指数$H\in (1/3,1)$的分数布朗运动。一方面，当$H=1/2$时，建立了$\widehat\theta_N$的若干收敛性结果。另一方面，当$H\neq 1/2$时，基于$\widehat\theta_N$的斯柯罗霍德积分型估计量无法从数据中直接计算，但本文针对$\widehat\theta_N$的一种可计算近似形式建立了若干收敛性结果。